3 Description

F08CKF (DORMRQ) is intended to be used following a call to F08CHF (DGERQF), which performs an RQ factorization of a real matrix A and represents the orthogonal matrix Q as a product of elementary reflectors.

This routine may be used to form one of the matrix products

QC, QTC, CQ, CQT,

overwriting the result on C, which may be any real rectangular m by n matrix.

A common application of this routine is in solving underdetermined linear least squares problems, as described in the F08 Chapter Introduction, and illustrated in Section 9 in F08CHF (DGERQF).

On exit: C is overwritten by QC or QTC or CQ or CQT as specified by SIDE and TRANS.

10: LDC – INTEGERInput

On entry: the first dimension of the array C as declared in the (sub)program from which F08CKF (DORMRQ) is called.

Constraint:
LDC≥max1,M.

11: WORK(max1,LWORK) – REAL (KIND=nag_wp) arrayWorkspace

On exit: if INFO=0, WORK1 contains the minimum value of LWORK required for optimal performance.

12: LWORK – INTEGERInput

On entry: the dimension of the array WORK as declared in the (sub)program from which F08CKF (DORMRQ) is called.

If LWORK=-1, a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued.

Suggested value:
for optimal performance, LWORK≥N×nb if SIDE='L' and at least M×nb if SIDE='R', where nb is the optimal block size.